TRANSACTIONS OF SECTION A. 551 



higher of these points operate on Q, the highest of Q Qj, and contrariwise. Draw 



OQ' inclined to OQ at an angle +a or —a. Draw the ordinate Q' M', and cut 



off P' M' = PM. P' is a point on the new curve corresponding to P on Ewing's 



curve. 



In this manner figures have heen drawn for the primary and secondary circuits 



of a secondary generator for cases where the acceleration and retardation of phase 



T , T 

 are— and -. 

 8 4 



In all these curves work is done in a complete cycle by the electric circuit on 



the iron when the curve is traced in a direction contrary to the motion of the 



hands of a watch, and contrariwise. We can now notice several facts : — 



(1) In all diagrams for the primary circuit the curves are described in the 

 same direction as Ewing's curve, showing that it does work on the iron. 



(2) In both diagrams for the secondary circuit the curve is described in the 

 opposite direction to Ewing's curve, showing that work is done by the iron on the 

 circuit. 



T 



(3) When the acceleration of the primary is — no work is done by the iron on 



the primary circuit at any part of the cycle. 



. T . 



(4) When the retardation of the secondary is — no work is done by the circuit 



upon the iron at any part of the cycle. 



(5) In the diagram for the secondary circuit, if the retardation be the angle 

 corresponding to the abscissa OA, the curve passes through the origin, and the 

 work done in a cycle is zero (A being the point where Ewing's curve cuts the 

 axis of abscissae). 



(6) If the retardation be less than this, work is done in the cycle by the 

 secondary circuit on the iron core. 



(7) It follows from this that, owing to magnetic hysteresis, the retardation of 

 the secondary current cannot be less than the angle corresponding to the abscissa 

 OA except in so far as it derives energy by direct induction from the primary. 



In most early attempts to make secondary generators the mutual induction of 

 the primary and secondary coils was very shght, and here the retardation must be 

 at least equal to the angle indicated. 



These remarks hardly apply to the secondary generator of Gautard & Gibbs, 

 who made it a commercial success mainly by causing the direct mutual ind-uction of 

 the circuits to be a maximum. 



Lord Rayleigh has pointed out that since the hysteresial dissipation of energy 

 per unit volume of iron is the same whether the magnetic circuit be open or 

 closed, while the total work done on or by the electric circuits is greater with an 

 open magnetic circuit, therefore the most efficient secondary generator is one with 

 an open magnetic circuit. This is true only when hysteresial dissipation is the 

 only cause of the loss of efficiency. It has appeared, however, that in actual 

 secondary generators hysteresial dissipation is but a portion of the cause of loss of 

 efficiency. Eesistance of the generator itself is a principal cause, and the loss from 

 this cause varies as the square of the current, and would be much greater with the 

 high currents proposed by Lord Rayleigh for his elongated elliptical iron core than 

 in a secondary generator with a closed iron magnetic circuit. The efficiency which 

 Lord Rayleigh proposes to gain in hysteresial dissipation is proportional to the 

 current. The loss due to resistance is proportional to the square of the current. 



Throughout this investigation I have assumed that magnetic induction does not 

 lag behind the magnetic force. 



The second part of this paper has relation to the molecular hypothesis. This 

 hypothesis as developed by Weber and Maxwell gives no account of hysteresis. 

 Ewing has proposed a further assumption — that a molecule has a friction (not a 

 viscous friction, but what "VMiewell called stiction) which prevents it from turning 

 until the turning force exceeds a constant value C 



It seems to me that the fewer assumptions we make the more near to the truth 



